%   ORIGINAL: 'h4/thm/rich_list/LUPDATE_APPEND1_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !l1 l2 n x. 'h4/const/prim_rec/<' n ('h4/const/list/LENGTH' l1) ==> 'h4/const/list/LUPDATE' x n ('h4/const/list/APPEND' l1 l2) = 'h4/const/list/APPEND' ('h4/const/list/LUPDATE' x n l1) l2
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !l1 l2 n x. 'h4/const/prim_rec/<' n ('h4/const/list/LENGTH' l1) ==> 'h4/const/list/LUPDATE' x n ('h4/const/list/APPEND' l1 l2) = 'h4/const/list/APPEND' ('h4/const/list/LUPDATE' x n l1) l2
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f55986,V_3f55982]: ![F, G]: (![X]: s(V_3f55982,happ(s(fun(V_3f55986,V_3f55982),F),s(V_3f55986,X))) = s(V_3f55982,happ(s(fun(V_3f55986,V_3f55982),G),s(V_3f55986,X))) => s(fun(V_3f55986,V_3f55982),F) = s(fun(V_3f55986,V_3f55982),G))).
fof('h4/thm/rich_list/LUPDATE_APPEND1_', conjecture, ![A]: ![L1, L2, N, X]: (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',N),s('h4/type/num/num','h4/const/list/LENGTH'(s('h4/type/list/list'(A),L1)))))) => s('h4/type/list/list'(A),'h4/const/list/LUPDATE'(s(A,X),s('h4/type/num/num',N),s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),L1),s('h4/type/list/list'(A),L2))))) = s('h4/type/list/list'(A),'h4/const/list/APPEND'(s('h4/type/list/list'(A),'h4/const/list/LUPDATE'(s(A,X),s('h4/type/num/num',N),s('h4/type/list/list'(A),L1))),s('h4/type/list/list'(A),L2))))).
